Monte Carlo study of hysteretic response for the two dimensional Ising system: scaling behavior

Abstract

In a Monte Carlo study of the two dimensional Ising system (of size 100 × 100) with nearest neighbour ferromagnetic interaction in the presence of a sinusoidally varying external magnetic field, we studied the variation of the hysteretic loop area (A) with frequency (f), amplitude (h₀) of external applied magnetic field and the temperature (T) of the system. We found the loop area A to scale as A ω h^β₀;T-^β;g(f/h^γ ₀;T^δ),for the entire range of the parameter variations considered. The best fit was obtained for β = 0.95 +-0.06, B = 0.60 +-0.03, γ = (1.65 ± 0.05) and δ = 1.05 ± 0.05 with the scaling function having the form g(x) ≈ x³ exp(-²x/ σ), ε ≅ 0.36. In the zero frequency limit, this result reduces to a power law fit and the exponents agree fairly well with the previous Monte Carlo estimates in this limit.